Lecture 16 — By reason, and by what sensibly appears, the stars are proved to be spherical in shape

316 With regard to the shape of each star, the most reasonable view is that they are spherical. It has been shown that it is not in their nature to move themselves, and, since nature is no wanton or random creator, clearly she will have given things which possess no movement a shape particularly unadapted to movement. Such a shape is the sphere, since it possesses no instrument of movement. Clearly then their mass will have the form of a sphere.

317 Again, what holds of one holds of all, and the evidence of our eyes shows us that the moon is spherical. For how else should the moon as it waxes and wanes show for the most part a crescent-shaped or gibbous figure, and only at one moment a half-moon? And astronomical arguments give further confirmation; for no other hypothesis accounts for the crescent shape of the sun's eclipses. One, then, of the heavenly bodies being spherical, clearly the rest will be spherical also.

441. After determining the nature, motion, and position of the stars, the Philosopher here determines about their shape. Concerning this he does two things:

first he shows by reason that the stars are spherical in shape;

secondly, by what is apparent to sense, at again, what holds of one (291b17; [445]).

442. He says therefore first (291b11), that someone can reasonably suppose that the figure of each star is spherical not only on the ground that they are of the nature of the heaven, as he proved above, but also because it has been shown above that the stars are not apt to be moved of themselves but are moved by the movements of their circles or spheres. Now nature does not do anything irrational or to no purpose, since the whole activity of nature is coordinated by an intellect acting for an end. Hence, it is plain that to the immovable stars, i.e., to those that are not moved on their own, this intellect gave a figure that is in no way suitable for progressive motion. Such a shape is, as he said above, the spherical, for the reason that it possesses no organ to serve for progressive motion. Yet, such a figure is most suitable for that type of circular motion in which the moved thing in its wholeness does not change its place. Thus it is plain that the stars, according to the mass of their magnitude, are spherical in figure.

443. But this proof does not seem to be appropriate. For Aristotle proved above that the stars are not moved on their own, on the ground that they are spherical in shape—hence, when he now proves that they are spherical in shape on the ground that they cannot be moved on their own, he seems to be arguing in circles. Alexander's answer to this is that nothing inappropriate follows from this—for Aristotle proved that the stars are not moved on their own, not only because they are spherical in shape but also through certain other middle terms. Likewise, he shows that the stars are spherical in shape through certain other middles and not only because they are of themselves immobile.

444. Simplicius, however, argues against this that the charge of circular demonstration is not removed by the fact that both conclusions are shown by several middles. But it should be stated that, although the notion of a circular demonstration is not thereby removed, yet there is removed the unacceptable situation arising from circular demonstration, namely, that it shows nothing. For the only way to manifest something is to use what is better known—and of course the same thing cannot be both better known and less known. However, when both conclusions are manifested by other middles, then one can be taken as manifestive of the other, in order to show the convertibility of the conclusions.

445. Then, at again, what holds of one (291b17) he presents another argument for the same, based on what is sensibly apparent, and he supposes that as one star is, so all the others are. There is shown then, by one of them, namely, the moon, from the things apparent to sense, that it is spherical in shape. This he shows in two ways.

First, from what is generally considered by all, namely, from the shapes the moon goes through in waxing and waning. For he says that unless the moon were spherical in shape, then, as it waxes and wanes, it would not appear most of the time as having the shape of a crescent or scimitar, or amphicurtos [gibbous], or also dichotomous. Some explain that the moon is said to be dichotomous when it is full, because it is then that it divides the month in half—for "dichotomous" refers to cutting in two. But this explanation conflicts with something that Aristotle will say later, namely, that we see the moon, when it is dichotomous, entering Mars and hiding it according to its dark part, but leaving according to its bright and shining part. From this it is clear that the moon is called "dichotomous" when its surface which is facing us is divided into two parts such that half is dark and half bright. This is also the meaning given to this word in Ptolemy's Synthesis translated from the Greek.

446. It is worthy of note that Aristotle makes no mention here of the shape which the moon has at the beginning or end of its waxing or waning, but only of the shape it has while it is waxing or waning. For, since the moon is spherical in shape, one of its hemispheres is always being illuminated by the sun and the other remains dark. When, therefore, the moon is in conjunction with the sun, its whole upper hemisphere, which is directly regarded by the sun, is illuminated by the sun, so that its lower hemisphere remains dark. It is then that the moon is seen by us as darkened and obscured. But as the moon gradually gets away from the sun, that part of its upper hemisphere which is farther from the sun ceases to be illuminated, and the lower hemisphere begins to be illuminated according to the same amount. At that time the moon appears crescent-shaped, i.e., arc-shaped. This goes on until it is a quadrant, i.e., a quarter circle, distant from the sun, and then its surface toward us is seen with one half dark and one half illuminated, and this makes it "dichotomous." After that, as the moon moves to opposition with the sun, more and more of its lower hemisphere begins to be illumined by the sun, and then it is called amphicurtos [gibbous] until it is in opposition with the sun. For at this time its entire lower hemisphere is illuminated by the sun and it is called "full." After that, it begins gradually to wane little by little until it is a quadrant distant, at which time it is called "dichotomous," as though half of it is bright. This brightness afterwards, when it diminishes below half, becomes crescent-shaped, until conjunction with the sun. Thus it is plain that as it waxes it is frequently or "mostly" arc-shaped or crescent-shaped, or gibbous; it is dichotomous just once as it is waxing and once in waning, namely, when it is distant from the sun by a quarter of a circle.

447. Now all this would not happen if the moon were not spherical in shape. For it is plain that if its surface turned toward us were totally flat, it would begin to be illumined by the sun all at once, and also to get dark, instead of successively by a continuing increase and decrease. This shows that it has a spherical bulge by which its brightness or darkness comes to be increased little by little—which could not happen if it were any shape but spherical.

448. Secondly, he shows the same thing from astronomical observations, which reveal that the eclipses of the sun are crescent-shaped, i.e., arcuate. For the sun begins to be obscured according to the figure of an arc, by the interposition of the moon between us and the sun. But this would not occur unless the moon were spherical, for spherical bodies cut each other according to arc-shaped sections, as is proved by mathematicians.

Therefore, if the situation is such with respect to one star, namely, the moon, it follows that all the other stars are also spherical in shape. This, of course, is based on all the stars' being of the same nature.

449. However, Averroes, in his Commentary, says that they are of the same specific nature, in such a way that all the stars are as individuals of the same species. Now this is plainly false.

First, because if they were all of the same species, they would have the same specific operations and the same effects, as is evident in all natural things of the same species.

Secondly, because, since the movements of the heavenly bodies are natural, it would follow that all the heavenly bodies would have uniform motions; but this is not true either of the planets in relation to one another, or in relation to the fixed stars.

Thirdly, because such a thing conflicts with the perfection of heavenly bodies. For in book I Aristotle proved that the universe is perfect on the ground that it is one—for it is one in one species. From this fact one sees that it consists of the total matter of its species.

Hence this also pertains to the perfection of the heavenly bodies, namely, that there be only one in one species. For we observe in the case of the lower bodies that there are many individuals of one species, on account of some lack of power or because one individual cannot exist forever—hence the species must be preserved by means of the succession of individuals in the same species. It is also because one individual is not sufficient for the perfect operation of the species—as is especially evident among men, one of whom is aided by another in his operation. Moreover, the multiplication of species, since it is formal, pertains more to the perfection of the universe than does the multiplication of individuals, which is material.

It is plain, too, that the reason which Averroes gives is absurd. For he says that if heavenly bodies were diverse species of one genus it would follow that the heavenly bodies would be material. However, this would much more follow if we posited, as he desires, the diverse heavenly bodies to be diverse individuals of the same species, because multiplication of individuals in one species is made through the division of matter. However, matter is not to be wholly excluded from the heavenly bodies. For it does not follow, even if the heavenly bodies have matter, that they are generable and corruptible, as was had in book I.

Consequently, it must be said that the heavenly bodies are one in nature according to genus but of diverse natures according to species. Now their spherical shape, as well as their circular motion, follows in them upon the nature of the genus.